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Construction of \(\text{G}^1/\text{C}^2\) continuous \(B\)-spline surfaces over arbitrary quadrilateral network. (Chinese. English summary) Zbl 1199.68465

Summary: For the point cloud or mesh model with quad-partition, an algorithm of constructing smooth joining \(B\)-spline surfaces over arbitrary quadrilateral network is developed. Firstly, a curve network is constructed over the quad-partitioned model. Then for each quadrilateral patch, a \(B\)-spline surface is fitted from four boundary curves and internal data points. After obtaining \(\text{G}^0\) continuous surface patches network, a method of modifying the cross-boundary derivatives is proposed to make two adjacent surfaces to be \(\text{C}^2\) continuous along regular edges or \(\text{G}^1\) continuous along irregular edges. Applications show that the presented algorithm is efficient and practical, and it has no restriction on the topology structure of the quadrilateral network; the reconstructed surfaces not only have good continuity but also capture the geometric details of the model and can satisfy the engineering requirements.

MSC:

68U07 Computer science aspects of computer-aided design
65D17 Computer-aided design (modeling of curves and surfaces)
65D07 Numerical computation using splines
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